Sign pattern matrices that allow orthogonality
type: Item
instance of: scholarly article
title: Sign pattern matrices that allow orthogonality
zbMATH Open document ID: 0852.15018
DOI: 10.1016/0024-3795(94)00098-0
author: Charles Waters
published in: Linear Algebra and its Applications
publication date: 1996-12-16T00:00:00Z
review text: Two row (column) vectors with entries \(+,-,0\) are said to allow orthogonality, if they are the sign patterns of two orthogonal vectors in \(\mathbb{R}^n\). The author investigates square sign pattern matrices with no zero row and no zero column such that any two distinct rows and any two distinct columns are allowing orthogonality. Any such matrix is called sign potentially orthogonal (SPO). The question is whether every SPO matrix \(A\) allows orthogonality, i.e. \(A\) is the sign pattern matrix of an orthogonal matrix. The answer is negative due to an ad hoc counterexample of a \(5\times 5\) SPO-matrix that does not allow orthogonality. On the other hand sufficient conditions are given for an SPO-matrix to allow orthogonality.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 871107
zbMATH Keywords: sign pattern matrices
zbMATH Keywords: orthogonality
zbMATH Keywords: orthogonal matrix
zbMATH Keywords: counterexample
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00098-0
OpenAlex ID: W2093606493
cites work: Q4067293
cites work: Matrix Analysis
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description: scientific article; zbMATH DE number 871107